The model of random interlacements was recently introduced by Alain-Sol Sznitman as a natural tool to understand the trace left by a random walk in a discrete cylinder or in a discrete torus. In these contexts, this model describes the microscopic “texture in the bulk” left by the random walk when it is let run up to certain time scales. In this talk we are going to discuss some percolative properties of the vacant set of random interlacements under small intensities (e.g. the size of a finite vacant cluster). The results which will be presented could shed some light on problems such as how a random walk trajectory disconnects a discrete cylinder into two infinite connected components.